Just got myself echo show 5. I have ring doorbell all set up with it. When there is motion, I get notification on the ring app on my phone but nothing comes up on the echo show. Everything is set up as it should be.
According to the Ring Alexa Skill description, it looks like they haven't added the Echo Show 5 on the list of compatible devices. You may want to reach out to them to express your interest in seeing it added to their Alexa Skill functionality or ask if they have a planned release date for such an update.